OFFSET
0,1
COMMENTS
This entry completes the values of the derivatives eta'(z) at z = 0,1,i,-1,-i (see crossrefs).
LINKS
Stanislav Sykora, Table of n, a(n) for n = 0..2000
Eric Weisstein's World of Mathematics, Dirichlet Eta Function
FORMULA
eta'(-1) = 3*log(A) - log(2)/3 - 1/4, where A = A074962 is the Glaisher-Kinkelin constant.
EXAMPLE
0.265214370914704351169348273575616405600275762885520266292673582574...
MATHEMATICA
RealDigits[3*Log[Glaisher] - Log[2]/3 - 1/4, 10, 120][[1]] (* G. C. Greubel, Apr 09 2016 *)
RealDigits[DirichletEta'[-1], 10, 110][[1]] (* Eric W. Weisstein, Jan 06 2024 *)
PROG
(PARI) \\ Derivative of Dirichlet eta function (fails for z=1):
derdireta(z)=2^(1-z)*log(2)*zeta(z)+(1-2^(1-z))*zeta'(z);
derdireta(-1) \\ Evaluation
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Stanislav Sykora, Apr 09 2016
STATUS
approved